A new connection between WIMP dark matter and the hierarchy problem

TL;DR

This work investigates a direct link between the electroweak hierarchy problem and WIMP dark matter by proposing that the Higgs mass is dynamically driven toward the WIMP scale, placing the electroweak vacuum near a TeV-scale instability boundary. Using a higgsino-like singlet-doublet WIMP model, the authors show that DM Yukawa couplings modify the running of the Higgs quartic, lowering the instability scale $\mu_I$ and producing a metastability bound on the Higgs mass that correlates with the DM relic abundance. They demonstrate that DM masses $\gtrsim 1.2$ TeV imply a strong metastability bound and an upper bound on the scale $\Lambda$ of heavy new physics required to restore vacuum stability, with this scale potentially accessible via direct detection, indirect signals, and future colliders. The framework—combining a naturally split spectrum of vector-like fermions and cosmological vacuum-selection ideas—predicts TeV-scale new physics tied to the Higgs potential, offering concrete experimental targets across DM searches and collider programs.

Abstract

This work proposes a direct link between the hierarchy problem and Weakly Interacting Massive Particles (WIMPs): we suggest that the small mass of the Higgs boson arises from being dynamically driven to the scale of the WIMP. Such a special electroweak vacuum is singled out by lying close to the critical boundary of a phase transition, as recently explored in a new class of cosmological solutions to the hierarchy problem. They generically predict the Higgs potential to be destabilised just above the weak scale. Intriguingly, the requirement for new physics to achieve this coincides with two independently well-motivated expectations: a split spectrum of light fermions and heavy bosons, as anticipated from naturalness, and the so-called "WIMP miracle". A WIMP with mass around the weak scale not only happens to have the correct thermal relic abundance to be the dark matter (DM), it can also give rise to the necessary critical boundary at the TeV scale through its Yukawa couplings to the Higgs. We use a higgsino-like singlet-doublet model to illustrate our Higgs-DM criticality scenario and show that if this WIMP DM mass is observed to be greater than ~1.2 TeV then it necessarily implies a strong bound on the Higgs mass and an upper bound on the scale of heavy new physics that restores vacuum stability. It can be thoroughly probed in direct detection experiments, astrophysical signals and future collider searches, further motivating a comprehensive exploration of the remaining heavy WIMP parameter space.

Figures (10)

• Figure 1: Schematic summary of our near-critical Higgs DM scenario in which the Higgs mass is dynamically driven to the WIMP Scale. a) A split spectrum of naturally light fermions and heavy bosons is expected from naturalness, and thermal WIMP DM further motivates the existence of fermions around the weak scale. b) Such a split spectrum can destabilise the Higgs potential, since fermion Yukawa couplings contribute negatively to the renormalisation group running of the Higgs quartic while positive contributions from bosons are decoupled to heavier scales. c) This leads to an upper bound on the Higgs mass in order for our electroweak vacuum to exist. d) An underlying cosmological mechanism places the Higgs mass close to this critical boundary.
• Figure 2: Thermal dark matter relic density $\Omega_\text{DM}h^2$ in the blind spot with $\tan{\theta}=-1$. Left: Regions of the parameter space leading to DM over-production for $y=1.5$ (red) and under-production for $y=0.1$ (blue). The contours corresponding to the observed DM abundance are shown for Yukawa couplings $y=0.1$ (dash-dotted), $y=1.0$ (dotted) and $y=1.5$ (dashed). Contours of DM mass, $m_\mathrm{DM}$, in the mostly-doublet regime are represented by solid black lines. Right: Relic abundance contours for $y=1.0$ in the mostly-doublet regime. The black solid line corresponds to the observed relic density.
• Figure 3: Left: Sketch of the effective Higgs potential $V_{\rm eff}$ in Eq. \ref{['eq:Veff']} together with the effective quartic coupling $\lambda_{\rm eff}$. The coupling crossing zero due to its RG evolution leads to the potential turning over. Right: Sketch of the effective potential for a fixed RG-trajectory of $\lambda$ and three different values of the mass parameter.
• Figure 4: Metastability bound $m_\mathrm{crit}$ in the singlet and doublet mass plane for Yukawa couplings of $y=1$ (left) and $y=1.5$ (right) for $\tan{\theta}=-1$. The grey shaded region is mainly excluded by direct detection.
• Figure 5: Critical value of the Higgs mass parameter $m_\mathrm{crit}$ as a function of the Yukawa coupling and singlet mass of the singlet-doublet model. We consider the mostly-doublet DM regime with $m_D < m_S$, and choose the correspondingly lightest doublet mass giving rise to the observed DM relic abundance. The grey region is excluded by direct detection constraints or cannot reproduce the observed DM abundance.